if $f(x)$ and $f^{-1}(x)$ are inverse functions of each other and $f(x)=2x + 5$, what is $f^{-1}(8)$?\n-1\n$\…

if $f(x)$ and $f^{-1}(x)$ are inverse functions of each other and $f(x)=2x + 5$, what is $f^{-1}(8)$?\n-1\n$\frac{3}{2}$\n$\frac{41}{8}$\n23

if $f(x)$ and $f^{-1}(x)$ are inverse functions of each other and $f(x)=2x + 5$, what is $f^{-1}(8)$?\n-1\n$\frac{3}{2}$\n$\frac{41}{8}$\n23

Answer

Explanation:

Step1: Set up the equation

If (y = f(x)=2x + 5) and we want to find (f^{-1}(8)), we set (y = 8) in the original - function and solve for (x). So, (8=2x + 5).

Step2: Solve for (x)

Subtract 5 from both sides of the equation: (8−5=2x+5 - 5), which simplifies to (3 = 2x). Then divide both sides by 2: (x=\frac{3}{2}). Since if (y = f(x)) then (x = f^{-1}(y)), when (y = 8), (f^{-1}(8)=\frac{3}{2}).

Answer:

(\frac{3}{2})